The Coupling between Quantum Mechanics and Elasticity

In this dissertation we explore the junction of quantum mechanics and elas- ticity. Specifically, we attempt to elucidate, in several physical contexts, how me- chanical deformation alters the quantum mechanical behavior of nanostructures and nanomaterials. In the first part of the dissertation, we develop a theoretical framework which shows that a striking analog of the electrostatic Maxwell stress also ex- ists in the context of quantum mechanical-elasticity coupling. The newly derived quantum-elastic Maxwell stress is found to be significant for soft nanoscale struc- tures (such as the DNA) and underscores a fresh perspective on the mechanics and physics of quasi-particles called polarons. We discuss potential applications of the concept for soft nano-actuators and sensors and the relevance for the inter- pretation of opto-electronic properties. Mechanical strain can alter the electronic structure of both bulk semicon- ductors as well as nanostructures such as quantum dots. We relate the notion of polarons and the previously mentioned quantum-Maxwell stress to optoelec- tronic coupling. This effect, while negligible for hard materials, emerges to be important for soft materials and critically impacts the interpretation of quanti- ties such as polaron size, binding energy, and accordingly, electronic behavior in entities like DNA, polymer chains among others. A rather interesting ramification of quantum mechanics-elasticity coupling transpires in the context of the so-called "quantum capacitance". One of the many tantalizing recent physical revelations about quantum capacitance is that it can possess a negative value, hence allowing for the possibility of enhancing the over- all capacitance in some particular material systems beyond the scaling predicted by classical electrostatics. Using detailed quantum mechanical simulations, we find an intriguing result that mechanical strains can tune both signs and values of quantum capacitance. Finally, in the context of DNA like slender structures, we explore how quantum mechanical-elasticity coupling may impact the stability of such soft nanostructures.Mechanical Engineering, Department o